He was also dismissive of the resolution’s prospects for success, telling Talking Points Memo that he “[didn’t] see [Obama] agreeing to defund his signature issue.”

Back in July, Graham had referred to defunding ObamaCare as "a bridge too far" for him.

A spokesman for Graham said that the senator had always supported defunding ObamaCare, but simply rejected a strategy that involved shutting down the government. He also said Graham was rejecting the strategy, advocated by Senator Ted CruzRafael (Ted) Edward CruzUp next in the culture wars: Adding women to the draft Biden's bipartisan deal faces Senate gauntlet 228 Republican lawmakers urge Supreme Court to overrule Roe v. Wade MORE (R-Texas), that Senate Republicans immediately filibuster the House resolution in the Senate to prevent Democrats from invoking cloture and then re-adding funding for ObamaCare via a majority vote.

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Conservative backers of the plan to defund ObamaCare such as Sen. Mike LeeMichael (Mike) Shumway LeeThis week: Senate starts infrastructure sprint Senators introduce bipartisan infrastructure bill in rare Sunday session Biden's bipartisan deal faces Senate gauntlet MORE (R-Utah) have denied any intent to trigger a government shutdown, saying the only people willing to shut the government down are Democrats who refuse to back a spending resolution unless it funds ObamaCare. Lee, Cruz, and Marco RubioMarco Antonio RubioSenate holds sleepy Saturday session as negotiators finalize infrastructure deal Break glass in case of emergency — but not for climate change Democrats join GOP in pressuring Biden over China, virus origins MORE (R-Fla.), the leading proponents of the defunding effort, all endorsed the House's resolution.

Graham is currently facing multiple primary challengers who accuse the senator of being too centrist. In late August, several Tea Party groups began a series of online ads attacking him for not committing to the defunding effort.